schoolswikiaorg-20200215-history
Bernoulli's Principle
Introduction You’re relaxing outside your house on a sweltering summer day. It’s not even noon and the temperature outside is close to 105˚. So because of this heat, a bunch of people walk over to the fire hydrant across the street and pry it open releasing a huge amount of water. For about 20 minutes the water is steadily streaming out wetting everything that it can in its path. After these 20 minutes the water isn’t being projected as far as it was in the beginning, meaning that it has lost its pressure. As time goes by, the pressure at which the water was coming out has gone down, but the velocity at which the water was coming out has increased rapidly. What has gone on with the fire hydrant is an example of the everyday phenomenon known as Bernoulli's principle. http://images.greencine.com/images/article/do-the-right-thing-water.jpg Bernoulli's Principle Bernoulli's principle basically states that when there is a decrease in pressure there must be an increase in velocity at the same rate that the pressure was decreased. The same is true if there is an increase in pressure, it must be accompanied by a decrease in speed. (In the case of physics, in this particular example, a fluid can be either a gas or a liquid.) The formula for Bernoulli's Principle is: Pressure + (kinetic energy/volume)= constant Bernoulli's principle can also be re-written as Pressure+(.5)(density)(velocity)^2=constant Venturi Tubes The following image is that of a venturi tube, which is a tube that is used frequently to illustrate the concept of Bernoulli's principle. A venturi tube is a tube that has three sections: a front, middle, and back, but in the middle, the tube narrows signficantly. When the fluid flows into the front of the tube, the speed is higher, therefore the pressure of the fluid is lower. When the fluid goes into the narrower middle section of the tube, the speed that the water flows into the tube is severely lower than when the fluid flows into the front, but the pressure has increased, thus proving Bernoulli's principle. When the fluid goes into the wider back section of the tube, the pressure is greatly decreased creating a higher velocity. http://www.mste.uiuc.edu/davea/aviation/ventouri.gif (A venturi tube.) Bernoulli's Life http://cepa.newschool.edu/het/profiles/image/bernoulli.jpg (Daniel Bernoulli) Daniel Bernoulli was born February 8th, 1700 in the town of Groningen in the Netherlands. Bernoulli was the son of Johann Bernoulli, a mathematician who was a teacher at the university of Groningen. In addition, his older brother and uncle were mathematicians as well. From the start Daniel Bernoulli was born into an accomplished family in the field of mathematics, but also into a family in which bitter jealousy and rivalries occurred among the men in the family. After much debate Daniel studied medicine at Heidelberg, and his father agreed to teach his son mathematics. After completing college, Daniel decided to fulfill a career in teaching, but he was unable to get a post, so he decided to go to Venice to work in medicine. When he arrived he became too ill to study medicine, and so as a direct result he decided to study mathematics. His first work was published in 1724 when he was working for the mathematician Christian Goldbach. It was called Mathematical exercises and it was divided into four separate sections about four mathematical topics that had interested him while he was in Venice. The next part of his publication had to do with the flow of water, when the water was flowing from a hole in any type of container. In this work he discussed the theories of Sir Isaac Newton, and had stated that they were incorrect. But despite having stated that Newton's theories were incorrect, he had no evidence to prove this, and because of that this was first step into what would eventually lead him to make a monumental discovery. In late 1725, Daniel, along with his brother, went to St. Petersburg to co-chair mathematics. But within, eight months of their appointment his brother had died, and this loss had devastated him. The person who filled his brother's part was a pupil of his brother, a mathematician, named Leonard Euler, famous for his discovery of the number e''. During this period while working at St. Petersburg, he discovered the concept of nodes on oscillating systems, meaning places of no movement on systems that continuously moved in the same direction such as the sine curve and music waves. He also made the important discovery of Bernoulli's principle. Bernoulli eventually went back to the town where his family had all originated from called Basel, where he taught, lectured, created new theories, and was constantly lauded by his peers in the scientific community. He died in Basel on March 17, 1782. Bernoulli's Discovery As previously mentioned above the most important work that Daniel Bernoulli had was his work in the field of hydrodynamics. His discovery was the first time that an analysis of water flowing from a hole in a container was correct. His discovery was that, as iterated above, that a rise in pressure would cause a decrease in speed and a decrease in pressure would cause an increase in speed. Bernoulli largely created his principal based on the theory of conservation of energy. (The law of conservation of energy states that energy can be neither created nor destroyed, and therefore the sum of all the forms of energy in the system is constant.) He used the conservation of energy as well as pumps and other machines that are used to raise water to come up with this principle. Applications of Bernoulli's Principle Bernoulli's Principle has several various modern day applications in the world around us. The following section discusses where, and in what applications can you see this principle take place. 'Airflight: One of the most common everyday applications of Bernoulli's principle is in airflight. Almost everyone in the world has seen an airplane in the sky, and everyone has probably at one point in their lives, asked themselves how does it fly? With Bernoulli's principle we can answer this question. The main way that Bernoulli's principle works in air flight has to do with the architecture of the wings of the plane. In an airplane wing, the top of the wing is soomewhat curved, while the bottom of the wing is totally flight. While in the sky, air travels across both the top and the bottom concurrently. Because both the top part and the bottom part of the plane are designed differently, this allows for the air on the bottom to move slower, which creates more pressure on the bottom, and allows for the air on the top to move faster, which creates less pressure. This is what creates lift, which allows planes to fly. http://www.mste.uiuc.edu/davea/aviation/foil.gif (This diagram shows how in the plane the top of the airplane is slightly curved which allows for faster moving air and less pressure, and the bottom is flat, which allows for slower moving air, and more pressure.) Lift: One of the most common trends that occurs in the modern day physics world is that of lift. Lift can be seen in many different ways, shapes, and forms in our world. Lift is seen in airflight, as in my example above, as well as in several of my forthcoming examples. But , what is lift exactly? Most people define lift in terms of Bernoulli's principle which has some validity to it, but the main way for one to define lift is through Newton's three laws. While most accept that Bernoulli's principle is what creates lift, some say that it leaves many unanswered questions. For one, it says that upside down flight cannot happen. Also, many people say that by using Bernoulli's principle to explain lift, it doesn't take into account the fact that no where in the commonly accepted defenition of lift, is there any mention of work, and lift can only take place if there is a certain type of unit of work that we are all familiar with, called power. The next most widely accepted definition of lift involves Newton's three laws, specifically his first and third. (The first is the law of intertia and the third is that for every acton there is an equal and opposite raction.) As we have all seen on an airplane, the wing moves up and down a little bit as it flies through the air, but under the common defintion of lift, this cannot happen; the wing just stays still. Many physics scholars believe that there must be some form of movement on the object that is being lifted. http://www.allstar.fiu.edu/aerojava/images/sav4a.gif (The following illustration shows a theory on lift based on Bernoulli's principle in culmination with Newton's three laws.) For further reading on the different definitions of lift please visit http://www.allstar.fiu.edu/aerojava/airflylvl3.htm. '''Baseball: Baseball is an example of where Bernoulli's principle is very visible in everyday life, but rarely do most people actually take note of it. One example in baseball is in the case of the curve ball. The entire pitch works because of Bernoulli's principle. Since the stitches of the ball actually form a curve, it is necessary for the pitcher to grip the seams of the baseball. The reason as to why this is a necessity is that by gripping the baseball this way, the pitcher can make the ball spin. This allows for friction to cause a thin layer of air to engulf the baseball as it is spinning, but since the ball is spinning in a certain manner, this allows for more air pressure on the top of the ball and less air pressure on the bottom of the ball. Therefore, according to Bernoulli's principle there should be less speed on the top of the ball than there is on the bottom of the ball. What transpires is that the bottom part of the ball accelearates downwards faster than the top part, and this phenomenon allows for the ball to curve downward, which causes the batter to miscalculate the ball's position. http://wings.avkids.com/Book/Sports/Images/baseball.gif (An example of how Bernoulli's priinciple allows for a curve ball to be thrown.) For more information on how a baseball curves through the aid of Bernoulli's principle, please see http://www.pbs.org/safarchive/4_class/45_pguides/pguide_405/4545_bb.html 'Draft:' And furthermore, another example of Bernoulli's principle in our everyday lives is in the case of someone feeling a draft. We all at at least one time or another, have experienced feeling a draft, and it is because of Bernoulli's principle that we feel this draft. Let's say that in your room, you are really hot, but you know that it is nice and cool both outside your window and outside your door. If you open up your window, to try and let fresh air in, there won't be much of a temperature change, unless the door to your room is open to air out the hot air. The reason why it works this way, and this concept illustrates Bernoulli's principle is that if the front door is closed is that the door will become an area of high pressure, whereas right outside the door there is little pressure, meaning that the rate at which the air enters will be in an incredibly high speed. When you open the door, warm air flows out at high speed, thus indicating a reduction in pressure. With the warm air gone the cool air can now enter into the room, which thus creates a draft. 'Sailing' In addition to the three items above, Bernoulli's principle is also the governing theory that is behind sailing. Most people believe that sailing is just having a big sail and that when you put it up, the wind just takes your boat and drags it along the sea. This is not 100% correct. This is true only in the cases when the boat is moving with the wind, otherwise it is not true. When the boat does not travel with the wind, it usually moves perpendicular to the wind, and the boat moves not because the wind drags it along, but because of the concept of lift, which as mentioned above and in the case of airplanes, is what happens when either a liquid or a gas act on an object. The same way that Bernoulli's principle works for creating lift in airplanes, it works for creating lift in sails. All sail boats have two parts to it: a sail which points north and a keel which points on the opposite direction. If the speed of the air increases on the sail, there is less pressure on the sail, and conversely there is less pressure on the keel but a higher speed. Just like with an airplane this produces lift and proples the sail to move in the water. Aerodynamics In no other field of physics does Bernoulli's principle lend itself more than to the field of aerodynamics. However, before I can proceed with defining Bernoulli's principle in terms of aerodynamics, it is necessary for me to first define the term aerodynamics. Aeorydynamics is fluid dynamics that is concerned with the study of gas flow, and the majority of it has to do with finding different properties of flow: velocity, pressure, density, and temperature. Most people who study aerodynamics find these properties in terms of their relation to space and time. Aerodynamics are necessary in many fields where we see Bernoulli's principle at work, such as in sailing, where aerodynamics is used to predict the forces that act upon a sail. 'Architecture:' The concept of aerodynamics go hand-in-hand when one is talking about architecutre, particularly urban architecture and civil engineering, but many other forms of it as well. Before I go on, let me just take a minute to define civil engineering. Civil engineering is a branch of engineering which, according to its wiki page, "deals with the planning, construction, and maintenance of fixed structures or public works." (For more info on civil engineering please visit http://en.wikipedia.org/wiki/Civil_engineering.) The main way that cvil engineers use aerodynamics is that they use it to figure out how much wind can any structure that they build sustain. The term for the amount of wind that a particular structure can hold is referred to as its wind load. This particular aspect of urban aerodynamics helps architects and engineers ensure safety in buildings, both outdoor and indoor, while at the same time ensuring that the designs for a particular building or structure are state of the art. At this point, you may be asking yourself, what does this have to do with Bernoulli's principle? Well, it has a lot to do with Bernoulli's principle. Civil engineers use Bernoulli's principle to figure out a wind load for a structure, and ensure that a wind load does not topple or capsize a particular structure. For more reading on aerodynamics, please visit http://en.wikipedia.org/wiki/Aerodynamics. Review Problems Water flows steadily through a pipe out of an open tank. The elevation of point 1 (at the top of the tank) is 10 m and the elevation of points 2 and 3 is 2 m (in the pipe). The cross sectional area of point 2 is 0.0300 m2; and at point 3 it is 0.150 m2 (the pipe is narrowing). The area of the tank is very large in comparison to the pipe. If Bernoulli’s equation applies find: 1. the speed of the water at point 3 2. the speed of the water at point 2 3. the gauge pressure at point 2 http://www.science.ubc.ca/~csp/life/StudentSamples/Website2/tank.jpg Check your answers at http://www.science.ubc.ca/~csp/life/StudentSamples/Website2/index.html Resources and References References 1.http://theoryx5.uwinnipeg.ca/mod_tech/node68.html 2.http://uk.encarta.msn.com/encyclopedia_761557396/Aerodynamics.html 3.http://www.seykota.com/rm/Bernoulli_approach/index.htm 4.http://www-history.mcs.st-andrews.ac.uk/Biographies/Bernoulli_Daniel.html 5.http://www.allstar.fiu.edu/aerojava/airflylvl3.htm 6.http://www.mste.uiuc.edu/davea/aviation/bernoulliPrinciple.html 7. http://en.wikipedia.org/wiki/Civil_engineering Resources 1. http://en.wikipedia.org/wiki/Aerodynamics 2. http://en.wikipedia.org/wiki/Bernoulli%27s_principle 3. http://www.science.ubc.ca/~csp/life/StudentSamples/Website2/index.html (particularly an animated demo to help fully understand the concept of Bernoulli's principle.) 4. http://www.seykota.com/rm/Bernoulli_approach/index.htm 5. http://en.wikipedia.org/wiki/Lift_(force) 6. http://en.wikipedia.org/wiki/Civil_engineering Image Sites 1. cepa.newschool.edu/het/profiles/image/bernoulli.jpg (Image of Daniel Bernoulli) 2. www.mste.uiuc.edu/davea/aviation/ventouri.gif (Image of Venturi Tube) 3. images.greencine.com/images/article/do-the-right-thing-water.jpg (Image of fire hydrant in the beginning, from the 1989 film Do The Right Thing).) 4. www.mste.uiuc.edu/davea/aviation/foil.gif (Image of the airplane wing.) 5. www.allstar.fiu.edu/aerojava/images/sav4a.gif (Image of another airplane wing) 6. wings.avkids.com/Book/Sports/Images/baseball.gif (Image of the curve ball)